Equilibrium Paths of Mechanical Systems with Unilateral Constraints Part Ii: Deployable Reflector

The paper presents a simulation of the deployment/retraction of a solid surface deployable reflector recently developed at Cambridge University. The simulation takes proper account of the contacts that can develop between panels of adjacent wings of the reflector, by implementing the theory for tracing the equilibrium path of a mechanical system with unilateral constraints that has been proposed in the companion paper. Six-fold symmetry is assumed, as experiments on a physical model of the reflector show that asymmetries do not play a significant role. During deployment, at a certain point the model shows a sudden increase in the rate of motion although the (slow) rate of turning of the electric motors driving the model remains uniform. It is shown that the reason for this behaviour, which had not been previously explained, is the existence of a corner limit point on the equilibrium path of this structure. A corner limit point is a kind of limit point that can be encountered only in systems with unilateral constraints; the equilibrium path is non-smooth and the first-order equilibrium equations non-singular. A second limit point, of the standard type, exists on the equilibrium path. It should cause the model to jump to a configuration close to fully folded, but cannot be achieved in practice. A characteristic conical shape of the physical model is observed at the end of the retraction and is predicted by the simulation as well. (